Rényi entropy is an information-theoretic measure of randomness which is fundamental to several applications. Several estimators of Rényi entropy based on k-nearest neighbor (kNN) based distances have been proposed in literature. For d-dimensional densities f , the variance of these Rényi entropy estimators of f decay as O(M), whereM is the sample size drawn from f . On the other hand, the bias...

We discuss a basic thermodynamic properties of systems with multifractal structure. This is possible by extending the notion of Gibbs–Shannon’s entropy into more general framework Rényi’s information entropy. We show a connection of Rényi’s parameter q with the multifractal singularity spectrum f (α) and clarify a relationship with the Tsallis–Havrda–Charvat entropy. Finally, we generalize Hage...

We present a computational algorithm for isotrigon texture discrimination. The aim of this method consists in discriminating isotrigon textures against a binary random background. The extension of the method to the problem of multitexture discrimination is considered as well. The method relies on the fact that the information content of time or space-frequency representations of signals, includ...

We consider the problem of approximating the empirical Shannon entropy of a highfrequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is the Rényi entropy that depends on a constant α. This quantity can be estimated efficiently and unbiasedly from a low-dimensional synopsis called an α-stable da...

This paper is a follow-up of a recent work by Bobkov and Chistyakov, obtaining some improved Rényi entropy power inequalities (R-EPIs) for sums of independent random vectors. The first improvement relies on the same bounding techniques used in the former work, while the second significant improvement relies on additional interesting properties from matrix theory. The improvements obtained by th...